Hi Rachel,
I would first multiply both sides of the expression by 5(1 + y^{2}) to get
5xy^{3} = 8(1 + y^{2})
At this point the problem is very similar to the question you sent a couple of days ago. As in that problem you need to see the variables, here x and y, as functions of time t. As the particle moves along the curve both x and y change.
You are told that when the particle is at (1,2) the xcoordinate is increasing at the rate of 6 units per second. That means that when x = 1 and y = 2 you know that dx/dt = 6 units per second. You are asked to find dy/dt at that instant.
As in your previous problem you need to differentiate both sides of the equation with respect to t. This will give you an equation involving x, y, dx/dt and dy/dt. Since you know x, y and dx/dt at the instant in question you can find dy/dt.
Penny
